Gordon Brown and David Cameron were involved in a bitter clash in the Commons this afternoon over the death of Baby P.

After Cameron said the case showed that Haringey council was incapable of looking after children and criticised Brown for failing to answer his questions about the affair, the prime minister retaliated by accusing him of exploiting the story for party-political advantage.

The prime minister did not withdraw it, but he did not repeat the charge and he said there was "common ground" in the Commons over the response to "this very sad and tragic case".

The Conservative leader asked about Haringey because it was the local authority responsible for the care of Baby P, who died despite 60 visits by health and social care workers over an eight-month period.

Baby P, who was on the child protection register, died in August last year after suffering more than 50 injuries. His mother, her partner and another man have been convicted of involvement in his death.

Sharon Shoesmith, the chairwoman of the Haringey safeguarding children board, said that three professionals had received formal written warnings in connection with the case.

Lord Laming, who called for a series of reforms in the wake of her death, described the similarities a "dispiriting".

At prime minister's questions today Cameron said: "I want to ask about the tragic death of Baby P.

"This happened in the same children's services department that was responsible for Victoria Climbié and yet again nobody is taking responsibility, nobody has resigned.

"Do you agree with me that the Haringey inquiry is completely unacceptable?

"It is being led by Mrs Shoesmith, who is the council's own director of children's services. Do you agree with me she cannot possibly investigate the failure of her own department?"

Brown replied: "I believe I speak for the whole country when I say that people are not only shocked and saddened, but horrified and angered by what they have seen reported about what happened to an innocent 17-month-old boy.

"Every child is precious and every child is unique. Every child should have the benefit of support and protection both from their parents and the authorities that be.

"This tragedy that has arisen because of a violence and torture of a young child, where three have already been found guilty, raises serious questions we have to address."

Brown said that Laming has now been asked to produce a new report considering what needed to be done to improve child protection throughout the country. And Brown said that the full report into the affair from Haringey had only arrived on the desk of the children's secretary, Ed Balls, this morning.

"It is now for the government to take action and we will make a decision about what procedures and processes we will adopt in relation to Haringey," he said.

But the mood of the exchange turned bitter as Cameron pressed Brown about the Haringey review. He asked Brown to accept that it was "completely unacceptable" for Shoesmith to be investigating her own department.

As Labour MPs nosily protested, Michael Martin, the Speaker, intervened, saying: "Please let Mr Cameron be heard. It will not do [to have] shouting across the chamber after this terrible news has come to us. It's best to let him speak."

Cameron went on: "I'll tell you what is shameful and that is trying to shout down someone who's asking reasonable questions about something that's gone wrong."

Stabbing the dispatch box with his finger, he said: "Let's be honest. This is a story about a 17-year-old girl [Baby P's mother is actually 27] who had no idea how to bring up a child.

"It's about a boyfriend who couldn't read but could beat a child and it's about a social services department that gets £100m a year and can't look after children.

"In the case of failing schools we take them over. This department in Haringey, one in four positions for social workers is completely vacant. They do nothing to help struggling local schools that are failing and another child has been beaten to death."

He said to Brown: "Will you - I don't expect an answer now; you never get one - at least consider whether the time has come to take over this failing department and put someone in charge who can run it properly for our children."

Brown replied: "I think we are both agreed this is a tragic and serious loss of life that has got to be investigated properly so that all the lessons can be learned …

"We have received the full report this morning. We will act on it quickly. We will do it in the right way so that we come to the judgments that are necessary to protect children in the future.

"I do regret making a party-political issue of this issue. I do regret that because I think ..."

Brown was then drowned out by opposition protests. But the Speaker said that the prime minister was in order.

Brown went on: "Because I think the whole country shares the outrage, the whole country wants to see action and the whole country will support the action that is being taken nationally and in relation to Haringey."

Earlier Beverley Hughes, the children's minister, called for further investigations of Haringey council. She said that more examination of the senior management levels at the north London borough was needed to see if anyone should take responsibility for the death of Baby P.